|Speaker:||Kentaro Nagao (Nagoya University)|
|Title:||Donaldson-Thomas theory and cluster algebras|
|Date (JST):||Mon, Jun 28, 2010, 14:00 - 17:00|
In the first part, I will talk on the Donaldson-Thomas theory associated to a quiver with a potential (non-commutative Donaldson-Thomas theory). A quiver with a potential provide a 3-dimensional Calabi-Yau category and a t-structure of it. The Donaldson-Thomas invariant is the (weighted) Euler characteristic of the moduli space of objects in the category. I will introduce a transformation formula which tells us how the invariant depends on the choice of a t-structure.
In the second part, I will talk on a skech of the proof using the theory of the motivic Hall algebra and an application to the theory of cluster algebras. A cluster algebra is an subalgebra of the field of rational functions together with a certain system of generators. It has been discoverd that the theory of cluster algebras has many links with a wide
range of mathematics. The structure of cluster algebras appear in the transformation formula and we can naturally understand the properties of cluster algebras from the view point of the Donaldson-Thomas theory.